Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression
This paper proposes numerical solutions of Hamilton-Jacobi inequalities based on constrained Gaussian process regression. While Gaussian process regression is a tool to estimate an unknown function from its input and output data conventionally, the proposed method applies it to solving a known parti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2018-09-01
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| Series: | SICE Journal of Control, Measurement, and System Integration |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.9746/jcmsi.11.419 |
| _version_ | 1797661000052244480 |
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| author | Kenji Fujimoto Hirofumi Beppu Yuji Takaki |
| author_facet | Kenji Fujimoto Hirofumi Beppu Yuji Takaki |
| author_sort | Kenji Fujimoto |
| collection | DOAJ |
| description | This paper proposes numerical solutions of Hamilton-Jacobi inequalities based on constrained Gaussian process regression. While Gaussian process regression is a tool to estimate an unknown function from its input and output data conventionally, the proposed method applies it to solving a known partial differential inequality. This is done by generating sample data pairs of states and corresponding values of the unknown function satisfying the inequality. A formal algorithm to execute such a procedure to obtain the probability of a solution to the Hamilton-Jacobi inequality is proposed. In addition, a nonstationary covariance function is introduced to increase the accuracy of the solutions and to reduce the computational cost. Furthermore, its hyper parameters are optimized using an empirical gradient method. |
| first_indexed | 2024-03-11T18:39:04Z |
| format | Article |
| id | doaj.art-afb2c44bcd8046c68c043d6904d6fd3c |
| institution | Directory Open Access Journal |
| issn | 1884-9970 |
| language | English |
| last_indexed | 2024-03-11T18:39:04Z |
| publishDate | 2018-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | SICE Journal of Control, Measurement, and System Integration |
| spelling | doaj.art-afb2c44bcd8046c68c043d6904d6fd3c2023-10-12T13:43:55ZengTaylor & Francis GroupSICE Journal of Control, Measurement, and System Integration1884-99702018-09-0111541942810.9746/jcmsi.11.41912103234Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process RegressionKenji Fujimoto0Hirofumi Beppu1Yuji Takaki2Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto UniversityDepartment of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto UniversityDepartment of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto UniversityThis paper proposes numerical solutions of Hamilton-Jacobi inequalities based on constrained Gaussian process regression. While Gaussian process regression is a tool to estimate an unknown function from its input and output data conventionally, the proposed method applies it to solving a known partial differential inequality. This is done by generating sample data pairs of states and corresponding values of the unknown function satisfying the inequality. A formal algorithm to execute such a procedure to obtain the probability of a solution to the Hamilton-Jacobi inequality is proposed. In addition, a nonstationary covariance function is introduced to increase the accuracy of the solutions and to reduce the computational cost. Furthermore, its hyper parameters are optimized using an empirical gradient method.http://dx.doi.org/10.9746/jcmsi.11.419nonlinear controloptimal controlhamilton-jacobi inequalitiesgaussian processes |
| spellingShingle | Kenji Fujimoto Hirofumi Beppu Yuji Takaki Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression SICE Journal of Control, Measurement, and System Integration nonlinear control optimal control hamilton-jacobi inequalities gaussian processes |
| title | Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression |
| title_full | Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression |
| title_fullStr | Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression |
| title_full_unstemmed | Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression |
| title_short | Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression |
| title_sort | numerical solutions of hamilton jacobi inequalities by constrained gaussian process regression |
| topic | nonlinear control optimal control hamilton-jacobi inequalities gaussian processes |
| url | http://dx.doi.org/10.9746/jcmsi.11.419 |
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